Periodic HartreeâFock linear combination of crystalline orbitals ...

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7212 C A Perottoni et al3.6(a)3.4Lattice parameter (Å)3.23.02.82.6-60 -40 -20 0 20 40 60 80 100 120 140Pressure (GPa)1.121.11(b)1.10c/a ratio1.091.081.071.061.051.04-60 -40 -20 0 20 40 60 80 100 120 140Pressure (GPa)Figure 3. (a) The pressure dependence of the TiB 2 lattice parameters a (full circles) and c (opencircles). (b) The c/a ratio as a function of pressure. The solid curves in (a) show the fitting of theMurnaghan equation (3) for the lattice parameters.result in elastic constants significantly different from those quoted in table 3. The deviationfrom zero deformation of the minimum in the energy curve for the calculation of c 33 , seen infigure 4, just means that the algorithm used to search for the structure of minimum energy wasnot exhaustively iterated. In any case, the correction for the lattice parameters, owing to thisobserved deviation, should amount to only about 0.5%.Among the five elastic constants of TiB 2 , the value of c 44 was particularly difficult to obtain,since its calculation involves a triclinic deformation of the hexagonal unit cell, increasing bya factor of four the number of points needed to interpolate the wavefunction in the irreducibleBrillouin zone (keeping a shrinkage factor of 12 in the Monkhorst net).Despite the large discrepancies between the reported experimental single-crystal elasticconstants for TiB 2 , the analysis of the data in table 3 can reveal some trends in our results.
Periodic HF-LCCO calculations for titanium diboride 72130.00240.00200.00160.00120.00080.00040.0000cc 11+c 12 11+c 12c11 11 +c +c12 120.00160.00120.0008Strain energy (Hartree)0.00040.00000.00400.00320.00240.00160.00080.0000c 11-cc 1211-c 12c 11 -c -c12 12c 13 13c 11 +c 12 +2c 13 +c 33 /20.00120.00080.00040.0000c 33 33c 33 /20.00120.00080.0004c 442c 44440.0000-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03Deformation parameter εFigure 4. The dependence of the strain energy on the adimensional lattice deformation parameterε. The inset in each panel shows the specific combination of elastic constants in the second-orderterm of the E(ε) expansion, from which the elastic constants were obtained [29].There is a good agreement between our values for c 13 and c 33 and those calculated by vanCamp and van Doren [13]. On the other hand, the value obtained by them for c 11 + c 12 isbetween 15 and 20% (depending on the particular functional used for the exchange–correlationcontribution to energy) smaller than our result. Our estimates for the elastic constants c 13 and
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Periodic HartreeâFock linear combination of crystalline orbitals ...